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XII: 37, 491-508, LNM 649 (1978)
Ensembles à coupes dénombrables et capacités dominées par une mesure (Measure theory, General theory of processes)
Let $X$ be a compact metric space $\mu$ be a bounded measure. Let $F$ be a given Borel set in $X\times R_+$. For $A\subset X$ define $C(A)$ as the outer measure of the projection on $X$ of $F\cap(A\timesR_+)$. Then it is proved that, if there is some measure $\lambda$ such that $\lambda$-null sets are $C$-null (the relation goes the reverse way from the preceding paper 1236!) then $F$ has ($\mu$-a.s.) countable sections, and if the property is strengthened to an $\epsilon-\delta$ ``absolute continuity'' relation, then $F$ has ($\mu$-a.s.) finite sections
Comment: This was a long-standing conjecture of Dellacherie (707), suggested by the theory of semi-polar sets. For further development see 1602
Keywords: Sets with countable sections
Nature: Original
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